Unrefinable partitions into distinct parts in a normalizer chain
Combinatorics
2022-05-25 v1 Group Theory
Abstract
In a recent paper on a study of the Sylow 2-subgroups of the symmetric group with 2^n elements it has been show that the growth of the first (n-2) consecutive indices of a certain normalizer chain is linked to the sequence of partitions of integers into distinct parts. Unrefinable partitions into distinct parts are those in which no part x can be replaced with integers whose sum is x obtaining a new partition into distinct parts. We prove here that the (n-1)-th index of the previously mentioned chain is related to the number of unrefinable partitions into distinct parts satisfying a condition on the minimal excludant.
Cite
@article{arxiv.2107.04666,
title = {Unrefinable partitions into distinct parts in a normalizer chain},
author = {Riccardo Aragona and Roberto Civino and Norberto Gavioli and Carlo Maria Scoppola},
journal= {arXiv preprint arXiv:2107.04666},
year = {2022}
}